Do we have a right to try to convince people to abandon demonstrably false, or socially harmful, opinions? Clearly we have no right to force them, but do we have the right to criticize their opinions and try and get them to engage with reality or with other human beings?
Conversely, do people have a duty to adopt true beliefs whenever they have the opportunity to do so knowingly?

I'm not sure about the rights language here but I can't imagine that there would be anything amiss with trying to dissuade someone of the notion that the earth is flat or that 2+2=5. As for adopting true beliefs, I'm not sure that we are put together so that we can choose my beliefs. If I know something to be true it would seem to imply that I believe it. But to be sure, there are a wide range of issues and some of the most important in life, in which what is true and false are beyond definitive proof.